General Engineering Dimensional Analysis

[Mikesgto]

The period T of a pendulum of length L, mass m in a gravitational field g ms-2 is suspected to be a function of L, m and g. If it is postulated that
T=KL^xm^yg^z
where K is a dimensionless constant, use dimensional analysis to obtain the constants x, y and z.

There's only one pi group I came up with and that was g/(T²L)

other than that, I can't figure out how to begin this problem in a way that will give me an opportunity to solve for the three exponents.

 

[Dickfore]

The period T of a pendulum of length L, mass m in a gravitational field g ms-2 is suspected to be a function of L, m and g. If it is postulated that
T=KL^xm^yg^z
where K is a dimensionless constant, use dimensional analysis to obtain the constants x, y and z.

There's only one pi group I came up with and that was g/(T²L)

other than that, I can't figure out how to begin this problem in a way that will give me an opportunity to solve for the three exponents.

Start by writing out the dimensions (mass, length, time) of each of the physical quantities involved.

 

[Mikesgto]

Ok so perhaps my attempt wasn't completely written above. I wrote down all the units, namely meters, m/s^2 for gravity and kg for mass. That's the only pi group I can think of but then I can't figure out the steps to solve for 3 individual exponents.

 

[Dickfore]

how about for T?

 

[Mikesgto]

Well T=1/s which is included in my original Pi group of g/(T^2*L). But once I have one pi group, which is all I can have because I have 4 variables and only 3 basic dimensions, how do I go about relating that to solving for the variables?

Correct me if I'm wrong, but mass should not play a factor in pendulum swings. And should I use the pendulum period equation from basic physics, neglecting drag etc.?

 

[Dickfore]

Ok, first of all, what is a "Pi group"?

Second, your dimension (unit) for the PERIOD T is incorrect?